The purpose of this paper is to consider the impulse formulations of the Euler equations for incompressible and compressible fluids. Different gauges are considered. In particular, the Kuz'min gauge provides an interesting case as it allows the fluid impulse velocity to describe the evolution of material surface elements. This result affords interesting physical interpretations of the Kuz'min invariant. Some exact solutions in the impulse formulation are studied. Finally, generalizations to compressible fluids are considered as an extension of these results. The arrangement of the paper is as follows: in the first chapter we will give a brief explanation on the importance of the study of fluid impulse. In chapters two and three we will derive the Kuz'min, E & Liu, Maddocks & Pego and the Zero gauges for the evolution equation of the impulse density, as well as their properties. The first three of these gauges have been named after their authors. Chapter four will study two exact solutions in the impulse formulation. Physical interpretations are examined in chapter five. In chapter six, we will begin with the generalization to the compressible case for the Kuz'min gauge, based on Shivamoggi et al. (2007), and we will derive similar results for the remaining gauges. In Chapter seven we will examine physical interpretations for the compressible case.

No / The paper presents an incompressible Smoothed Particle Hydrodynamics (SPH) model to investigate the wave overtopping of coastal structures. The SPH method is a grid-less Lagrangian approach which is capable of tracking the large deformations of the free surface with good accuracy. The incompressible algorithm of the model is implemented by enforcing the constant particle density in the pressure projection. The SPH model is employed to reproduce a transient wave overtopping over a fixed horizontal deck and the regular/irregular waves overtopping of a sloping seawall. The computations are validated against the experimental and numerical data and a good agreement is observed. The SPH modelling is shown to provide a promising tool to predict the overtopping characteristics of different waves. The present model is expected to be of practical purpose if further improvement in the spatial resolution and CPU time can be adequately made.

<p> The pressure gradients for sphere trains in 1 in. and 2 in. pipes have been measured with water flowing past the stationary spheres at Reynolds numbers (based on pipe diameter) from to 4 - 105 , and sphere/pipe diameter ratios ranging from 0.486 - 0.84. Two dimensionless pressure ratios have been derived so that the experimental results obtained can be generalised to any pipe diameter with the above constraints on Reynolds number and diameter ratio. Drag coefficients have also been calculated from pressure drop measurements for the 0.84 diam. ratio spheres in· 1 in. pipe. These have been compared with McNoun's drag coefficient. </p> <p> The application of the results to predict pressure gradients for sphere trains in any pipe diameter has been illustrated. </p> / Thesis / Master of Engineering (MEngr)

Yes / The paper employs a Reynolds-averaged Navier¿Stokes (RANS) approach to investigate the time-dependent wave breaking processes. The numerical model is the smoothed particle hydrodynamic (SPH) method. It is a mesh-free particle approach which is capable of tracking the free surfaces of large deformation in an easy and accurate way. The widely used two-equation k¿¿ model is chosen as the turbulence model to couple with the incompressible SPH scheme. The numerical model is employed to reproduce cnoidal wave breaking on a slope under two different breaking conditions¿spilling and plunging. The computed free surface displacements, turbulence intensities and undertow profiles are in good agreement with the experimental data and other numerical results. According to the computations, the breaking wave characteristics are presented and discussed. It is shown that the SPH method provides a useful tool to investigate the surf zone dynamics.

Ce travail concerne l’écoulement incompressible et stationnaire autour d’un cylindre semi-infini en rotation, et ses propriétés de stabilité linéaire. L’effet de la courbure et de la rotation sur la stabilité de cet écoulement est étudié de manière systématique. Avant d’étudier la stabilité, nous calculons d’abord l’écoulement de base. A grand nombre de Reynolds, une couche limite se développe le long du cylindre, ce qui permet d’utiliser l’approximation de couche limite des équations de Navier–Stokes. Ces équations dépendent de deux paramètres de contrôle sans dimension, le nombre de Reynolds (Re) et le taux de rotation (S), et sont résolues numériquement pour obtenir les profils de vitesse et de pression pour une large gamme des paramètres de contrôle. Une couche limite initialement mince s’épaissit avec la distance axiale; ainsi, son épaisseur devient comparable et finalement plus importante que le rayon du cylindre. Au-delà d’un certain taux de rotation, les effets centrifuges conduisent `a un jet de paroi le long d’une portion du cylindre. L’extension axiale de ce jet augmente avec le taux de rotation. L’intensité du jet augmente aussi avec S. Des analyses asymptotiques de l’écoulement à grande distance axiale et à fort taux de rotation sont aussi présentées. L’analyse de stabilité linéaire du précédent écoulement est effectuée dans l’approximation locale. Après une décomposition en modes normaux, les équations des perturbations sont transformées en un problème de valeur propre `a fréquence complexe (ω). Ce problème dépend de cinq paramètres sans dimension: Re, S, la distance axiale normalisée (Z), le nombre d’onde axial (α) et le nombre d’onde azimutal (m). Les équations de stabilité sont résolues numériquement pour étudier les régions instables dans l’espace des paramètres. On observe que de faibles taux de rotation ont un effet important sur la stabilité de l’écoulement. Cette forte déstabilisation est associée à la présence d’un mode quasi-marginal pour le cylindre fixe et qui devient instable pour de petites valeurs de S. Ce phénomène est confirmé par une analyse en perturbation `a petit S. Sans rotation, l’écoulement est stable pour tout Re < 1060, et pour Z > 0.81. Mais, en présence d’une faible rotation, l’instabilité n’est plus limitée par une valeur minimale de Re ou un seuil en Z. Les courbes critiques dans le plan (Z, Re) sont calculées pour une large gamme de S et les conséquences pour la stabilité de l’écoulement discutées. Enfin, un développement asymptotique pour le nombre de Reynolds critique est obtenu, valable aux grandes valeurs de Z. / This work concerns the steady, incompressible flow around a semi-infinite, rotating cylinder and its linear-stability properties. The effect of cylinder curvature and rotation on the stability of this flow is investigated in a systematic manner. Prior to studying its stability, we first compute the basic flow. At large Reynolds numbers, a boundary layer develops along the cylinder. The governing equations are obtained using a boundary-layer approximation to the Navier–Stokes equations. These equations contain two non-dimensional control parameters: the Reynolds number (Re) and the rotation rate (S), and are numerically solved to obtain the velocity and pressure profiles for a wide range of control parameters. The initially thin boundary layer grows in thickness with axial distance, becoming comparable and eventually larger than the cylinder radius. Above a threshold rotation rate, a centrifugal effect leads to the presence of a wall jet for a certain range of streamwise distances. This range widens as the rotation rate increases. Furthermore, the wall jet strengthens as S increases. Asymptotic analyses of the flow at large streamwise distances and at large rotation rates are presented. A linear stability analysis of the above flow is carried out using a local-flow approximation. Upon normal-mode decomposition, the perturbation equations are transformed to an eigenvalue problem in complex frequency (ω). The problem depends on five non-dimensional parameters: Re, S, scaled streamwise direction (Z), streamwise wavenumber (α) and azimuthal wavenumber m. The stability equations are numerically solved to investigate the unstable regions in parameter space. It is found that small amounts of rotation have strong effects on flow stability. Strong destabilization by small rotation is associated with the presence of a nearly neutral mode of the non-rotating cylinder, which becomes unstable at small S. This is further quantified using smallS perturbation theory. In the absence of rotation, the flow is stable for all Re below 1060, and for Z above 0.81. However, in the presence of small rotation, the instability becomes unconstrained by a minimum Re or a threshold in Z. The critical curves in the (Z, Re) plane are computed for a wide range of S and the consequences for stability of the flow described. Finally, a large-Z asymptotic expansion of the critical Reynolds number is obtained.

Au cours de ces dernières années les processeurs sont devenus de plus en plus complexes (plusieurs niveaux de cache, vectorisation,...), l’augmentation de la complexité fait que l’étude des performances et les optimisations sont eux aussi devenus de plus en plus complexes et difficiles à comprendre. Donc développer un outil de caractérisation simple et facile d’utilisation des performances d’applications, serait de grande valeur. Le Modèle Roofline [17] promet un début de réponse à ces critères, mais reste insuffisant pour une caractérisation robuste et détaillée. Dans la première partie de cette thèse, Nous allons développer plusieurs versions améliorées du Roofline, robustes et précises, en passant par une version du Roofline en fonction du temps, des blocs et enfin la nouvelle version du Roofline introduite dans la suite de caractérisation Vtune d’Intel. Pour valider ces modèles, nous utilisons le benchmark LINPACK, STREAM ainsi qu’une mini-application développée au cours de cette thèse, qui résout l’équation de l’advection et qui servira de prototype pour l’évaluation de codes hydrodynamiques explicites. Nous portons aussi cette mini-application sur les co-processeurs d’Intel Xeon Phi KNL et KNC. Dans la deuxième partie de cette thèse nous nous intéressons à la simulation d’impact de vagues, à l’aide de codes industriels compressibles et incompressibles. Nous rajoutons plusieurs fonctionnalités dans le code compressible FluxIC, nous effectuons un chaînage de codes incompressible et compressible et enfin nous introduisons un nouveau schéma numérique appelé liquide incompressible et gaz quasi-compressible, qui permet de réaliser une simulation d’impact d’une vague via un code incompressible avec une correction compressible dans les zones où la compressibilité du gaz est importante. / During recent years computer processors have become increasingly complex (multiple levels of cache, vectorization, etc), meaning that the study of performance and optimization is also becoming more complex and difficult to understand. So a simple and easy-to-use model aimed at studying the performance of applications would be of great value. The Roofline model [17] promises to meet this criteria, but it is insufficient for robust and detailed characterization.In the first part of this thesis, several improved versions of the Roofline model, that are more robust and accurate, are developed by going through theRoofline version as a function of time and block, and finally a new Rooflinemodel is implemented in the Intel Vtune characterization suite. To validate thenew models, the LINPACK andtextitSTREAM benchmarks are used, as wellas, a mini-application developed during this thesis that solves the advectionequation and serves as a prototype for the evaluation of explicit hydrodynamicsimulation codes. This mini-application is also ported to the new Intel XeonPhi KNL and KNC co-processors.Simulation of wave impact using compressible and incompressible industrialcodes is the focus of the second part of this thesis. Several functionalities are added to the compressible FluxIC code, and a chaining of compressible andincompressible codes is carried out. Finally, a new numerical scheme called"incompressible liquid and quasi-compressible gas" is introduced, which allowsthe simulation of wave impact using an incompressible code with a compressiblecorrection in areas where gas compressibility is significant.

A finite difference based solution method is derived for the velocity-pressure formulation of the two-dimensional incompressible Navier-Stokes equations. The method is proven stable using the energy method, facilitated by SBP operators, for characteristic and Dirichlet boundary condition implemented using the SAT technique. The numerical experiments show the utility of high-order finite difference methods as well as emphasize the problem of pressure boundary conditions. Furthermore, we demonstrate that a discretely divergence free solution can be obtained by use of the projection method.

Incompressible free-surface flows involving highly complex and violent phenomena are of great importance to the engineering industry. Applications such as breaking-wave impacts, fluid-structure interaction, and sloshing tanks demand an accurate and noise-free pressure field, and require large-scale simulations involving millions of computation points. This thesis addresses the need with the novel use of a graphics processing unit (GPU) to accelerate the incompressible smoothed particle hydrodynamics (ISPH) method for highly non-linear and violent free-surface flows using millions of particles in three dimensions. Compared to other simulation techniques, ISPH is robust in predicting a highly accurate pressure field, through the solution of a pressure Poisson equation (PPE), whilst capturing the complex behaviour of violent free-surface flows. However, for large-scale engineering applications the solution of extremely large PPE matrix systems on a GPU presents multiple challenges: constructing a PPE matrix every time step on the GPU for moving particles, overcoming the GPU memory limitations, establishing a robust and accurate ISPH solid boundary condition suitable for parallel processing on the GPU, and exploiting fast linear algebra GPU libraries. A new GPU-accelerated ISPH algorithm is presented by converting the highly optimised weakly-compressible SPH (WCSPH) code DualSPHysics and combining it with the open-source ViennaCL linear algebra library for fast solutions of the ISPH PPE. The challenges are addressed with new methodologies: a parallel GPU algorithm for population of the PPE matrix, mixed precision storage and computation, and extension of an existing WCSPH boundary treatment for ISPH. Taking advantage of a GPU-based algebraic multigrid preconditioner for solving the PPE matrix required modification for ISPH's Lagrangian particle system. The new GPU-accelerated ISPH solver, Incompressible-DualSPHysics, is validated through a variety of demanding test cases and shown to achieve speed ups of up to 25.3 times and 8.1 times compared to single and 16-threaded CPU computations respectively. The influence of free-surface fragmentation on the PPE matrix solution time with different preconditioners is also investigated. A profiling study shows the new code to concentrate the GPU's processing power on solving the PPE. Finally, a real-engineering 3-D application of breaking focused-wave impacting a surface-piercing cylindrical column is simulated with ISPH for the first time. Extensions to the numerical model are presented to enhance the accuracy of simulating wave-structure impact. Simulations involving over 5 million particles show agreement with experimental data. The runtimes are similar to volume-of-fluid and particle-in-cell solvers running on 8 and 80 processors respectively. The 3-D model enables post-processing analysis of the wave mechanics around the cylinder. This study provides a substantial step for ISPH. Incompressible-DualSPHysics achieves resolutions previously too impractical for a single device allowing for the simulation of many industrial free-surface hydrodynamic applications.

In this study, the impact of various flow models is assessed under free and forced convection: compressible versus incompressible models for a Pressurized Water Reactor, and Darcy's law vs full momentum equation for High Temperature Gas Reactor. Euler equations with friction forces and a momentum and energy source/sink are used. The geometric model consists of a one-dimensional rectangular loop system. The fluid is heated up and cooled down along the vertical legs. A pressurizer and a pump are included along the horizontal legs. The compressible model is assumed to be the most accurate model in this study. Simulations show that under forced convection compressible and incompressible models yield the same transient and steady-state. As free convection is studied, compressible and incompressible models have different transient but the same final steady-state. As Darcy's law is used, pressure and velocity steady-state profiles yield some differences compared to the compressible model both under free and forced convections. It is also noted some differences in the transient.

This thesis presents a preconditioned solenoidal basis method to solve the algebraic system arising from the linearization and discretization of primitive variable formulations of Navier-Stokes equations for incompressible fluid flows. The system is restricted to a discrete divergence-free space which is constructed from the incompressibility constraint. This research work extends an earlier work on the solenoidal basis method for two-dimensional flows and three-dimensional flows that involved the construction of the solenoidal basis P using circulating flows or vortices on a uniform mesh. A localized algebraic scheme for constructing P is detailed using mixed finite elements on an unstructured mesh. A preconditioner which is motivated by the analysis of the reduced system is also presented. Benchmark simulations are conducted to analyze the performance of the proposed approach.